Weak form quadrature element analysis of geometrically exact shells

•A quadrature element formulation for nonlinear analysis of shells is presented.•A geometrically exact shell model is employed.•The total Lagrangian updating scheme of rotational quaternion is adopted.•The locking problems can be avoided without additional efforts in the formulation.

This paper presents a weak form quadrature element formulation of the stress resultant geometrically exact shell model proposed by Simo. A total Lagrangian updating scheme of rotation is adopted by the use of rotational quaternion. In addition to its conciseness for the coincidence of discrete nodes and integration points, the weak form quadrature element formulation exhibits computational feasibility as well as avoidance of shear and membrane locking problems for its high-order approximation property in nonlinear shell analysis. Several numerical examples are presented to illustrate the effectiveness of the proposed formulation.